Complex child rotations in transform hierarchies (IK)

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Im trying to convert some monobehaviour IK code to ECS, but nested transform rotations are kicking my butt. Could someone take a look at my code below and see where my ECS conversion has failed? Im getting nonsensical behaviour as seen in the video below

The code is attached below, with the monobehaviour code in comments

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Getting closer but still somewhat funky and not correct. I would really love it if someone could take a look at where I messed up converting to Unity.Mathematics. Newest code below